Translation:I did not get the answer I was hoping for.
There's not much difference, they both mean something in the past and can in most cases be used interchangeably. I think there's a tendency to use the continuous (the '-ing') form in conversation more. The two main reasons to use the continuous past are to show an action in the past that started before the point in time being described (e.g. "It was raining when I stepped outside", where it's clear the rain started further into the past than the stepping outside) or to show an action in the past that went on for a significant length of time, rather than just a moment (e.g. "I was looking for my keys" vs. "I looked up when I heard the door").
So for this sentence, the difference is very slight, but "I was hoping for" gives more of an impression of someone hoping for something over a period of time, whereas "I hoped for" suggests hope for something at a moment in time. I wouldn't use "I hoped for" very often, because hope is usually an on-going feeling, but I might say something like "I hoped for a miracle when I opened the letter" to show a decisive moment of hope. On the other hand, if it's something I wanted for a while, it feels much more natural to use the continuous past and say something like "I was hoping for some good weather at last".